Two goals apiece from Sergi Canos and Lasse Vibe along with a late fifth from Jota extended the Bees' unbeaten away run to four games whilst ending Burton's six-game unbeaten run and leaving the Brewers just a point above the Championship relegation zone going into the international break.
Canos put the Bees in front after 10 minutes, sweeping home a right-wing cross from Romaine Sawyers, although Albion were incensed that referee Andy Madley had not pulled play back for a head injury to defender Kyle McFadzean on halfway.
Sordell, who spent Friday getting married as opposed to preparing for the game, was twice on hand to capitalise as Brentford's soft underbelly from set-pieces was exposed.
The January signing from Coventry nodded home after Woodrow's near-post flick-on from Lasse Vigen Christensen had come back out off the crossbar, and was in the right place at the right time to slide home a second just two minutes later as another Christensen corner caused problems for the Brentford defence.
Woodrow gave Albion the comfort of a two-goal lead to take into half-time when he superbly curled home a free-kick from just outside the box after Luke Murphy had been sent tumbling.
The Bees were stung into action for the second half and by just after the hour mark Burton's lead had disappeared, Vibe coolly slotting home after excellent work on the edge of the box by Jota and Canos sliding home from a tight angle to level.
Michael Kightly and Woodrow squandered a chance to put Albion back in front, Daniel Bentley making an excellent save to deny Burton's on-loan Burnley winger with Woodrow sending the rebound wide from a good position.
Within seconds Jota had rattled the post with a shot from the edge of the box, substitute Nico Yennaris twice denied from the rebound, before Brentford wrapped up victory inside the final 10 minutes.
A quick break down the left allowed substitute Florian Jozefzoon to drill the ball across the box, Vibe showing a superb touch to guide a first-time volley into the net inside the six-yard box.
Any chance for Albion to respond was snatched away a minute later as Vibe turned provider with a ball into the near post. Jota's run was not tracked by the Burton defence and the Brentford man was able to steer the ball home in front of the visiting fans celebrating a remarkable turnaround.